In digital communication systems, a signal is often transmitted to a receiver via a channel that may be described using a transfer function. The receiver may implement a filter whose transfer function is substantially the inverse of the channel transfer function in order to undo the effect of channel and facilitate recovery of the signal. FIG. 1A is a block diagram illustrating a receiver filter used to receive a signal transmitted through a linear channel. In the block diagram, the signal is transmitted through a linear channel 100. The relationship between the output, Y, and the input, X, is expressed as a linear equationY=aX+b  (Equation 1)where a and b are constant coefficients. The inverse of the linear equation,                     Z        =                              Y            -            b                    a                                    (                  Equation          ⁢                                          ⁢          2                )            
leads to a relatively straightforward implementation of receiver filter 102 using linear digital filters.
FIG. 1B is a block diagram illustrating a receiver filter used to receive a signal transmitted through a nonlinear channel. In the block diagram, the signal is transmitted through a nonlinear channel 104. The transfer function characterizing the channel in this case is expressed asY=aX+cX3+b  (Equation 3)
Although this is a simplified Volterra series limited to one cubic term, its inverse includes an infinite number of terms. Thus, the design of receiver filter 106 becomes complex, and cannot be easily achieved using conventional linear filters. Generally, the complexity of receiver filter design tends to increase for transfer functions that include higher order polynomials.
In reality, many transmission channels are nonlinear. The challenges involved in inverting the transfer functions of nonlinear channels make it difficult to design receiver filters. Signal degradation, distortion and instability are often results of suboptimal receiver filter design. It would be useful to have a technique that would overcome the problems associated with receiver design for nonlinear channels and would result in channel inverting filters that can be implemented more easily.